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Synonym: Heat Capacity Ratio (γ) = Adiabatic Index (γ) = Isentropic expansion factor (κ) = Isentropic exponent (κ)

Ratio between Isobaric heat capacity $\begin{array}{l}C_P\end{array}$ and Isochoric heat capacity $\begin{array}{l}C_V\end{array}$ :

(1)	$\begin{array}{l}\displaystyle \gamma = \frac{C_P}{C_V}\end{array}$

Since (1) is the ratio it can be equivalently represented by intensive properties:

(2)	$\begin{array}{l}\displaystyle \gamma = \frac{c_P}{c_V} = \frac{c_{Pm}}{c_{Vm}}= \frac{c_{Pv}}{c_{Vv}}\end{array}$

where

$\begin{array}{l}c_P\end{array}$	Isobaric molar heat capacity	$\begin{array}{l}c_{Pm}\end{array}$	Isobaric specific heat capacity	$\begin{array}{l}c_{Pv}\end{array}$	Isobaric volumetric heat capacity
$\begin{array}{l}c_V\end{array}$	Isochoric molar heat capacity	$\begin{array}{l}c_{Vm}\end{array}$	Isochoric specific heat capacity	$\begin{array}{l}c_{Vv}\end{array}$	Isochoric volumetric heat capacity

The Heat Capacity Ratio can be equivalently represented as ratio of Isothermal Compressibility $\begin{array}{l}\beta_T\end{array}$ and Isentropic Compressibility $\begin{array}{l}\beta_S\end{array}$ :

(3)	$\begin{array}{l}\displaystyle \gamma=\frac{c_P}{c_V}=\frac{\beta_T}{\beta_S}= \kappa\end{array}$

wich is often denoted as $\begin{array}{l}\kappa\end{array}$ and referred as Isentropic exponent.

The Heat Capacity Ratio for ideal gases is:

(4)	$\begin{array}{l}\displaystyle \gamma = 1 + \frac{2}{f}\end{array}$

where

$\begin{array}{l}f\end{array}$

number of molecular freedom degrees

Heat capacity ratio for various fluids ^[1]:

Temp	Fluid	$γ$	Temp	Fluid	$γ$	Temp	Fluid	$γ$
−181 °C	H₂	1.597	200 °C	Dry air	1.398	20 °C	NO	1.400
−76 °C		1.453	400 °C		1.393	20 °C	N₂O	1.310
20 °C		1.410	1000 °C		1.365	−181 °C	N₂	1.470
100 °C		1.404	15 °C		1.404		N₂
400 °C		1.387	0 °C	CO₂	1.310	20 °C	Cl₂	1.340
1000 °C		1.358	20 °C		1.300	−115 °C	CH₄	1.410
2000 °C		1.318	100 °C		1.281	−74 °C		1.350
20 °C	He	1.660	400 °C		1.235	20 °C		1.320
20 °C	H₂O	1.330	1000 °C		1.195	15 °C	NH₃	1.310
100 °C		1.324	20 °C	CO	1.400	19 °C	Ne	1.640
200 °C		1.310	−181 °C	O₂	1.450	19 °C	Xe	1.660
−180 °C	Ar	1.760	−76 °C		1.415	19 °C	Kr	1.680
20 °C	Ar	1.670	20 °C		1.400	15 °C	SO₂	1.290
0 °C	Dry air	1.403	100 °C		1.399	360 °C	Hg	1.670
20 °C		1.400	200 °C		1.397	15 °C	C₂H₆	1.220
100 °C		1.401	400 °C		1.394	16 °C	C₃H₈	1.130

In express analysis of petroleum fluids (including liquid water and vapour) the Heat Capacity Ratio can be assumed $\begin{array}{l}\gamma \sim 1.3\end{array}$ .

References

White, Frank M. (October 1998). Fluid Mechanics (4th ed.). New York: McGraw Hill. ISBN 978-0-07-228192-7.

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Isentropic expansion factor = κ

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